And as well I have another table (table3). In that table I have columns table1_id and table2_id. table1_id is a link to a row in table1 and table2_id is a link to a row in another table.

I want in my query to get only those results that are defined in table3. Only those that have table1 rowid in their table1_id column. There may not be any columns at all referring to a certain table1 rowid so in this case I don't want to receive them.

How can I achieve this goal?

Update: I tried the following query, which doesn't work:

SELECT rowid FROM table1
WHERE rowid IN (SELECT table1_id FROM table3 WHERE table1_id = table1.rowid)
ORDER BY RANDOM() LIMIT 1

Assuming you want to select more than just a rowid, you need to SELECT from a JOIN between the tables you're interested in. SQLite doesn't have the full set of standard JOIN functionality, so you'll need to re-work your query so it can use a LEFT OUTER JOIN.